Multimode Fiber Having Improved Index Profile

ABSTRACT

A graded index multimode fiber and method of producing the graded index multimode fiber utilize a technique of reducing an index profile of the core of the multimode fiber below a standard parabolic index profile. This can be done by changing dopant concentrations in the fiber core over the radius of the fiber core. The result is a multimode fiber having differential mode delay characteristics that are intentionally not minimized. The index profile can be reduced below the standard parabolic index profile over the entire radius of the core, or only for radii above a specified radius.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.12/627,752, filed Nov. 30, 2009 which claims priority to U.S.Provisional Application Ser. No. 61/118,903, filed on Dec. 1, 2008, theentirety of which is hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention is generally directed to optical fibers for use incommunications and more specifically directed to a multimode opticalfiber having an improved index-of-refraction profile.

BACKGROUND OF THE INVENTION

In modern fiber optic communication systems, light signals are guidedalong cylindrical waveguides, which take the form of thin fibers.Optical fibers are comprised of an inner core region surrounded by anouter cladding region, where the optical density of the core, measuredin terms of refractive index n₁, is higher than the refractive index n₂of the cladding, FIG. 1. The refractive index of the optical media canbe adjusted by introducing impurities (or dopants) during themanufacturing process. For glass optical fibers germanium is typicallyused to increase the refractive index of the core, but other impuritiescan be used or added.

Due to this difference in refractive index, light pulses travelingwithin the core of the fiber undergo total internal reflection each timethey strike the core-cladding interface and as a result, the lightsignal is confined or guided within the core. This type of opticalfiber, which has a uniform core refractive index is called step-indexfiber (SI-fiber). To facilitate high-speed data communications, the corediameter of SI-fiber is typically small (on the order of 9 microns),which is only several times larger the wavelength of the transmittedlight and consequently, an optical signal is constrained to travel in asingle path along the fiber axis. This type of fiber is calledsingle-mode fiber.

Alternatively, the core diameter of the optical fiber can be large incomparison to the wavelength of light, in which case light can traversethe core along many discrete optical paths, where each optical path iscalled a mode. This type of fiber is referred to as multimode fiber(MMF) and has a nominal core diameter of 50 or 62.5 microns. Typically,in MMF a pulse of light impinging on the input end of the fiberilluminates a relatively large spatial area of the core so that theoptical pulse propagates as the sum of many discrete optical modes. Dueto differences in path length between modes, portions of the opticalpulse energy will arrive at the output end of the fiber at differenttimes. As a result, the width of the pulse broadens, referred to asinter-modal dispersion. This degrades signal quality. To reduceinter-modal dispersion, the refractive index of the MMF core andcladding is graded such that the refractive index decreases continuouslywith radial distance r from the core axis according to the equation,

${n_{0}^{2}(r)} = \left\{ {{\begin{matrix}{{n_{1_{0}}^{2}\left\lbrack {1 - {2\left( \frac{r}{R} \right)^{\alpha}\Delta_{0}}} \right\rbrack},} & {r < R} \\{{{n_{1_{0}}^{2}\left( {1 - {2\Delta_{0}}} \right)} = n_{2}^{2}}\ ,} & {r \geq R}\end{matrix}{Where}},{\Delta_{0} = \frac{n_{1_{0}}^{2} - n_{2}^{2}}{2n_{1_{0}}^{2}}}} \right.$

The fiber parameter a has a value close to two (typically 1.9-2.1), anddefines the shape of the refractive index profile, shown in FIG. 2 forα=2. An ideal parabolic (or power law) refractive index profile of acore with a radius R_(ideal) will cause each of the modes traversing agraded-index MMF to arrive at the output end of the fiber at the sametime. Low order modes traveling close to the fiber axis encounter a highrefractive index, i.e., a more optically dense medium, and willtherefore propagate at a reduced speed. Higher order modes propagatingin the outer regions of the core will encounter lower refractive index(less dense medium) and will propagate faster.

FIG. 3 illustrates the modes propagating in a MMF having an idealparabolic refractive index profile. Each of the modes traverses asinusoidal path and all modes arrive at the output end of the fiber atthe same time. We see that the nodes of each of the modes are in phase.

The quality of the refractive index profile of a MMF can becharacterized using a standard test procedure specified inTIA-455-220-A. This standard specifies the test method for measuringdifferential mode delay (DMD), which quantifies the inter-modaldispersion. In this method, a single-mode launch fiber is stepped acrossthe core of a MMF and the propagation delay of each excited set of modestraversing the fiber is recorded. A plot of the DMD for ahigh-performance MMF is shown in FIG. 4.

The plot shows the recorded optical waveforms for each of the excitedsets of modes at the output of the fiber in picoseconds per meter (ps/m)as a function of radial launch position in microns on the vertical axis.For this representative MMF we see that each of the excited sets ofmodes arrives at the output of the fiber at about the same timeirrespective the optical launch radial position and therefore, thisfiber introduces little inter-modal dispersion. From the DMD plot onecan deduce that the refractive index profile for this fiber is near theideal parabolic profile.

However in practice, due to difficulties in controlling low dopantconcentrations during the manufacturing process, most MMF's do notexhibit ideal parabolic refractive index profiles. In particular, dopantconcentrations in the outer regions of the core where the concentrationsare smallest are most challenging to control. As a result, higher ordermodes often exhibit variations in mode delay in comparison to thosemodes propagating along the inner regions of the core. It is thereforedesirable to modify the refractive index profile in such a way as toreduce the adverse affect caused by variations in low level flow controlof dopant.

SUMMARY OF THE INVENTION

An important factor that affects the performance of an optical channellink is the amount of total dispersion in the fiber. To improve theperformance of MMF, a modification to the manufacturing process isproposed that alters the index profile to values below the refractiveindex that would normally be seen with a traditionally ideal parabolic αvalue. We describe a modification to the refractive index profile thathas been shown to improve measured system performance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cutaway perspective view of an optical fiber;

FIG. 2 is a graph showing the index of refraction versus radius in thecore and cladding of a graded-index multimode fiber;

FIG. 3 is a diagram showing mode behavior in a graded-index multimodefiber;

FIG. 4 is a differential mode delay diagram showing the relative time ofpulse arrival as compared to the radius offset in a multimode fiber;

FIG. 5 is a graph showing the index of refraction versus radius in thecore of a multimode fiber both according to the prior art (α₀) andaccording to the present invention (α); and

FIG. 6 is a differential mode delay diagram showing the differentialmode delay characteristics of a multimode fiber having an index profilemodified according to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The number of modes N, supported by the MMF is given by,

$N_{0} = {\frac{\alpha}{\alpha + 2}n_{1_{0}}^{2}k_{0}^{2}R^{2}\Delta_{0}}$

Where, k₀=2π/λ₀, is the wave number for light having wavelength λ₀ infree space. By changing the targeted value of the refractive indexprofile whereby it decreases to a lower than ideal parabolic value atincreasing radial distance in the core, improved fiber performance isachieved. According to one embodiment, the value of the refractive indexprofile is decreased below an ideal parabolic index profile. Accordingto a preferred embodiment, the refractive index profile is decreasedcontinuously and monotonically. In some embodiments, the targetrefractive index profile is altered above a specific core radius r_(i).For example, in one embodiment, the target refractive index profile isaltered for core radii greater than 5 μm such that the refractive indexprofile is smaller than the profile following a power law function (asshown in FIG. 5). In another embodiment, the target refractive indexprofile is altered for core radii greater than 1 μm.

According to one embodiment of the present invention, a technique isused to decrease the “target” value of the refractive index profile bycontrolling dopant concentrations to result in a decreased refractiveindex below what would traditionally result from a standardparabolic-type distribution. It has been discovered that, in cases wherea traditional ideal parabola is the target, a certain relatively smallamount of the resulting fiber will fall near the target, producing adesirable DMD plot as shown in FIG. 4.

However, due to the difficulty of controlling low concentrations ofdopant, the index profile of a certain amount of the produced fiber willfall below the target profile, and some of the fiber will have an indexprofile that falls above the target profile. Fibers that have indexprofiles in regions higher than the target parabolic profile (whichwould be characterized by a “shift to the right” with increasing radiusin the plot of FIG. 6) have poor System Bit Error Rate (BER)performance.

A fiber that has a modified refractive index profile as proposed willexhibit a DMD trace essentially similar to that shown in FIG. 6. As theradius increases beyond 8 microns in FIG. 6, there is a lateraldisplacement of the waveform peaks that shift continuously andmonotonically towards the left side of the graph. In this casehigher-order modes are traveling faster since a shift to the leftcorresponds to smaller values in units of ps/m.

In FIG. 5, we plot two refractive index profiles, α₀=2, and the proposedmodified profile shown by the dashed line. Here we use α₀=2 as anexample, but obviously this modification applies equally to values of αother than 2. The solid curve represents the variation of the refractiveindex that follows the equation of n₀(r) described above. The proposedmodified refractive index profile (dashed line) does not follow thatequation, and instead follows a different equation (for example denotedas n_(mod)(r)). A fiber that follows the n₀(r) described by the formulawill have a DMD trace similar to that shown in FIG. 4.

Such a modification to the refractive index will affect the supportednumber of modes N. If the fiber follows a power law,

${n_{0}^{2}(r)} = {{{n_{1_{0}}^{2}\left\lbrack {1 - {2\left( \frac{r}{R} \right)^{\alpha}\Delta_{0}}} \right\rbrack}\mspace{14mu} {for}\mspace{14mu} r} < R}$

With Δ₀ defined as

$\Delta_{0} = \frac{n_{1_{0}}^{2} - n_{2}^{2}}{2n_{1_{0}}^{2}}$

The supported number of modes is

$N_{0} = {\frac{\alpha}{\alpha + 2}n_{1_{0}}^{2}k_{0}^{2}R^{2}\Delta_{0}}$

Assuming that n₁ has a weak radial dependence, we could write n₁ as

n ₁(r)=n ₁ ₀ ²+ε(r)

In this case Δ becomes

$\Delta = \frac{n_{1_{0}}^{2} + {ɛ(r)} - n_{2}^{2}}{2\left\lbrack {n_{1_{0}}^{2} + {ɛ(r)}} \right\rbrack}$

Neglecting the ε(r) in the denominator, Δ becomes Δ(r)=Δ₀+ε(r).Replacing Δ(r) and n₁(r) in the equation for N, we get

$N = {\frac{\alpha}{\alpha + 2}{\left\{ {\left\lbrack {n_{1_{0}}^{2} + {ɛ(r)}} \right\rbrack k_{0}^{2}R^{2}} \right\} \left\lbrack {\Delta_{0} + {ɛ(r)}} \right\rbrack}}$

This results in four terms. The term that is proportional to ε² (r) canbe neglected. The same for the term proportional to ε(r)·Δ₀, since ε andΔ₀ are much smaller than n.The two remaining terms yield

$N = {{\frac{\alpha}{\alpha + 2}k_{0}^{2}R^{2}{n_{1_{0}}^{2}\left\lbrack {\Delta_{0} + {ɛ(r)}} \right\rbrack}} = {N_{0}\left\lbrack {1 + \frac{ɛ(r)}{\Delta_{0}}} \right\rbrack}}$

For a variation of ε(r) on the order of a tenth of Δ₀, and where ε(r) isa negative quantity, the number of supported modes is reduced byN=N₀×0.9. Or in this case the number of modes, N is reduced by 10%.Although higher-order modes travel faster increasing inter-modaldispersion the modification to the index profile according to someembodiments of the present invention will also result in higher systemperformance.

System measurements for fibers having a refractive index profileexhibiting a DMD plot where the pulse waveforms shift to the left atlarge radial offsets, as shown in FIG. 6, have shown improved fiberperformance as compared to the known technique of attempting to have therefractive index profile match an parabolic target. This target can beachieved by decreasing the α value for portions of the core fallingwithin a certain range of radii, or with radii falling above a certainnumber.

It has been found that altering the method of production of a multimodefiber as described herein, as compared to fibers having a “greater thanparabolic” refractive index profile, results in produced fibers having amore desirable BER performance. According to some measurements,multimode fibers made with target refractive index profiles having a“lower-going” profile within a radius range of the core, as shown inFIG. 5, can have BER performance of up to 1000× better than multimodefibers manufactured with a “higher-going” profile within the same radiusrange.

System measurements for fibers having a refractive index profileexhibiting a DMD plot where the pulse waveforms shift to the left atlarge radial offsets, as shown in FIG. 6, have shown improved fiberperformance as compared to the known technique of attempting to have therefractive index profile match a parabolic target. This target can beachieved by decreasing the α value (where α=β) for portions of the corefalling within a certain range of radii, or with radii falling above acertain number.

1. Method of selecting between a first fiber and a second fibercomprising: measuring a pulse delay for pulses traveling throughdifferent radii for the first fiber and the second fiber; and choosingbetween the first fiber and the second fiber a fiber which demonstratesa greater left shift for radii greater that a predetermined radius. 2.Method of selecting between a first fiber and a second fiber comprising:measuring a pulse delay for pulses traveling through different radii forthe first fiber and the second fiber; and choosing between the firstfiber and the second fiber a fiber which has a smaller pulse delay for apulse at a predetermined radius.
 3. Method of selecting between a firstfiber and a second fiber comprising: measuring a pulse delay for pulsestraveling through different radii for the first fiber and the secondfiber; and choosing between the first fiber and the second fiber a fiberwhich demonstrates smaller pulse delays for radii greater than apredetermined radius.